Ceist Eile

Ceist Eile is in development. Features, questions and prices may change while we refine it.

Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Recurrence relations & differences

How often Recurrence relations & differences comes up on the Applied Maths papers, every year it was asked, and questions to try.

OL Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Recurrence relations & differences, Ordinary Level(7 marks)

Quick ones on Recurrence relations & differences.

(a)uₙ₊₁ = uₙ + 5 and u₀ = 3. Find u₂.
  1. 8
  2. 13
  3. 18
(b)What is a recurrence relation?
  1. A list of numbers with no pattern
  2. The sum of all the terms in a sequence
  3. A rule giving each term from earlier terms
(c)uₙ₊₁ = 2uₙ and u₀ = 3. Find u₃.
  1. 24
  2. 48
  3. 12
Show the answers

(a) 13

(b) A rule giving each term from earlier terms

(c) 24

Your turn: Ordinary Level questions on Recurrence relations & differences.

Ordinary Level

Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q2
2024Q3
2023Q1

Links open the State Examinations Commission’s paper for that year.

More Recurrence relations & differences questions

Recurrence relations & differences, 2 marks

uₙ = 2n + 1. Which are the first three terms, u₁, u₂, u₃?

  1. 1, 3, 5
  2. 3, 6, 9
  3. 3, 5, 7
Show the answer

3, 5, 7

Substitute n = 1, 2, 3: 2(1) + 1 = 3, 2(2) + 1 = 5, 2(3) + 1 = 7. 1, 3, 5 starts from n = 0 instead of n = 1.

Recurrence relations & differences, 3 marks

A ball dropped from 10 m bounces to half its previous height each time. Distance travelled when it lands for the 3rd time?

  1. 20 m
  2. 25 m
  3. 17.5 m
Show the answer

25 m

Down 10, then up and down 5 + 5, then up and down 2.5 + 2.5: 10 + 10 + 5 = 25 m. 17.5 m counts each bounce once; 20 m stops at the 2nd landing.

Recurrence relations & differences, 3 marks

What is the next term of the geometric sequence 64, 48, 36, …?

  1. 27
  2. 24
  3. 18
Show the answer

27

Common ratio = 48 ÷ 64 = 0.75. Next term = 36 × 0.75 = 27. 24 subtracts 12 each time, treating it as arithmetic; 18 halves the last term.

Other Applied Maths topics

All of Leaving Cert Applied Maths